Geometry Unit 6 Note Sheets. Name of Lesson. 6.1 Angles of Polygons 1.5 days. 6.2 Parallelograms 1 day. 6.3 Tests for Parallelograms 1.
|
|
- Peregrine Hancock
- 5 years ago
- Views:
Transcription
1 Date Name of Lesson 6.1 Angles of Polygons 1.5 days 6.2 Parallelograms 1 day 6.3 Tests for Parallelograms 1.5 days Quiz days 6.4 Rectangles 1 day 6.5 Rhombi and Squares 1 day 6.6 Trapezoids and Kites 1 day Review and test 2 days 1
2 6.1 Quadrilaterals Notes Find the Interior Angles Sum of a Polygon Example 1: A. Find the sum of the measures of the interior angles of a convex nonagon. Example 1: B. Find the measure of each interior angle of parallelogram RSTU. Guided Practice 1: A. Find the sum of the measures of the interior angles of a convex octagon. Guided Practice 1: B. Find the value of x. 2
3 Example 2: ARCHITECTURE A mall is designed so that five walkways meet at a food court that is in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon. Guided Practice 2: A pottery mold makes bowls that are in the shape of a regular heptagon. Find the measure of one of the interior angles of the bowl. Find Number of Sides Given Interior Angle Measure Example 3: The measure of an interior angle of a regular polygon is 150. Find the number of sides in the polygon. Guided practice 3: The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon. 3
4 Find Exterior Angle Measures of a Polygon Example 4: A. Find the value of x in the diagram. Example 4: B. Find the measure of each exterior angle of a regular decagon. 4
5 Guided Practice 4: A. Find the value of x in the diagram. Guided Practice 4: B. Find the measure of each exterior angle of a regular pentagon. 5
6 6.2 Parallelograms Notes 6
7 Use Properties of Parallelograms Examples1: A. CONSTRUCTION In Find AD. ABCD suppose m B = 32, CD = 80 inches, BC = 15 inches. Examples 1: B. CONSTRUCTION In ABCD suppose m B = 32, CD = 80 inches, BC = 15 inches. Find m C. Example 1: C. CONSTRUCTION In Find m D. ABCD suppose m B = 32, CD = 80 inches, BC = 15 inches. Guided Practice 1: A. ABCD is a parallelogram. Find AB. Guided Practice 1: B. ABCD is a parallelogram. Find m C. Guided Practice 1: C. ABCD is a parallelogram. Find m D. 7
8 More practice: Find the value of each variable in the parallelogram
9 Use Properties of Parallelograms and Algebra Example 2: A. If WXYZ is a parallelogram, find the value of r. Example 2: B. If WXYZ is a parallelogram, find the value of s. Example 2: C. If WXYZ is a parallelogram, find the value of t. Guided Practice 2: A. If ABCD is a parallelogram, find the value of x. Guided Practice 2: B. If ABCD is a parallelogram, find the value of p. Guided Practice 2: C. If ABCD is a parallelogram, find the value of k. 9
10 More practice: Find the missing variables. 5. Parallelograms and Coordinate Geometry Example 3: What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M( 3, 0), N( 1, 3), P(5, 4), and R(3, 1)? Guided Practice 3: What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with vertices L(0, 3), M( 2, 1), N(1, 5), O(3, 1)? More examples: 6. Determine the coordinates of the intersection of the diagonals of parallelogram FGHJ with vertices F( 2, 4), G(3, 5), H(2, 3), and J( 3, 4). Steps: 1. Name the diagonals. 2. Find the midpoint of the diagonals. 10
11 11
12 6.3 Tests for Parallelograms Notes 12
13 Identify Parallelograms Example 1: Determine whether the quadrilateral is a parallelogram. Justify your answer. Guided Practice 1: Which method would prove the quadrilateral is a parallelogram? A. Both pairs of opp. sides. B. Both pairs of opp. sides.c. C. Both pairs of opp. s. D. One pair of opp. sides both and. Mores Examples: Determine whether the quadrilateral is a parallelogram. Justify your answer
14 Use Parallelograms to Prove Relationships Example 2: MECHANICS Scissor lifts, like the platform lift shown, are commonly applied to tools intended to lift heavy items. In the diagram, A C and B D. Explain why the consecutive angles will always be supplementary regardless of the height of the platform. Guided Practice 2: The diagram shows a car jack used to raise a car from the ground. In the diagram, AD BC and AB DC. Based on this information, which statement will be true, regardless of the height of the car jack. Use Parallelograms and Algebra to Find Values Example 3: Find x and y so that the quadrilateral is a parallelogram. Guided Practice 3: Find m so that the quadrilateral is a parallelogram. 14
15 More Examples: 4. If FK = 3x 1, KG = 4y + 3, JK = 6y 2, and KH = 2x + 3, find x and y so that the quadrilateral is a parallelogram. Example 4: COORDINATE GEOMETRY Graph Quadrilateral QRST has vertices Q( 1, 3), R(3, 1), S(2, 3), and T( 2, 1). Determine whether the quadrilateral is a parallelogram. Justify your answer by using the Slope Formula. Guided Practice 4: Graph quadrilateral EFGH with vertices E( 2, 2), F(2, 0), G(1, 5), and H( 3, 2). Determine whether the quadrilateral is a parallelogram. 15
16 More Examples: Graph each quadrilateral with the given vertices. Determine whether the figure is a parallelogram. Justify your answer. 7. K(2, 3), L(8, 4), M(7, 2), and N(1, 3) Steps: 1. Find the distance of each side. 2. Find the slopes of sides. Example 5: A student is given the following information and then asked to write a paragraph proof. Determine which statement would correctly complete the student s proof. Given: Parallelogram PRST and Parallelogram PQVU Prove: V S Proof: We are given Parallelogram PRST and Parallelogram PQVU. Since opposite angles of a parallelogram are congruent, P V and P S.. A. Therefore, V S by the Transitive Property of Congruence. B. Therefore, V S by the Transformative Property of Congruence. C. Therefore, V S by the Reflective Property of Congruence. D. Therefore, V S by the Reflexive Property of Congruence. 16
17 6.4 Rectangles Notes Example 1: CONSTRUCTION A rectangular garden gate is reinforced with diagonal braces to prevent it from sagging. If JK = 12 feet, and LN = 6.5 feet, find KM. Guided Practice 1: Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ. Use Properties of Rectangles and Algebra Example 2: Quadrilateral RSTU is a rectangle. If m RTU = 8x + 4 and m SUR = 3x 2, find x. 17
18 Guided Practice 2: Quadrilateral EFGH is a rectangle. If m FGE = 6x 5 and m HFE = 4x 5, find x. Proving Rectangle Relationships Example 3: ART Some artists stretch their own canvas over wooden frames. This allows them to customize the size of a canvas. In order to ensure that the frame is rectangular before stretching the canvas, an artist measures the sides and the diagonals of the frame. If AB = 12 inches, BC = 35 inches, CD = 12 inches, DA = 35 inches, BD = 37 inches, and AC = 37 inches, explain how an artist can be sure that the frame is rectangular. 18
19 Guided Practice 3: Max is building a swimming pool in his backyard. He measures the length and width of the pool so that opposite sides are parallel. He also measures the diagonals of the pool to make sure that they are congruent. How does he know that the measure of each corner is 90? More examples: A rectangular park has two walking paths as shown. 1. If PS = 180 meters and PR = 200 meters, find QT. 2. If m PRS = 64, find m SQR. 3. Using the rectangular park, if TS = 120 meters find PR. Example 4: Quadrilateral JKLM has vertices J( 2, 3), K(1, 4), L(3, 2), and M(0, 3). Determine whether JKLM is a rectangle using slopes. 19
20 Guided Practice 4: Quadrilateral WXYZ has vertices W( 2, 1), X( 1, 3), Y(3, 1), and Z(2, 1). Determine whether WXYZ is a rectangle by using the Distance Formula. More examples: 4. Quadrilateral PQRS has verticies P( 5, 3), Q(1, 1), R( 1, 4), and S( 7, 0). Determine whether PQRS is a rectangle. Find the area. 1. Find the distance of each side. 2. Find the distance of the diagonals. 3. Find the area. 20
21 5. What is the value of x in the rectangle? 6. What is the value of x in the rectangle? 21
22 6.5 Rhombi and Squares Notes Use Properties of a Rhombus Example 1: A. The diagonals of rhombus WXYZ intersect at V. If m WZX = 39.5, find m ZYX. Example 1: B. ALGEBRA The diagonals of rhombus WXYZ intersect at V. If WX = 8x 5 and WZ = 6x + 3, find x. 22
23 Guided Practice 1: A. ABCD is a rhombus. Find m CDB if m ABC = 126. Guided Practice1: B. ABCD is a rhombus. If BC = 4x 5 and CD = 2x + 7, find x. More Examples: The diagonals of rhombus FGHJ intersect at K. Use the given information to find the each measure or value. 1. If m FJH = 82, find m KHJ. 2. If GH = x + 9 and JH = 5x 2, find x. The diagonals of rhombus WXYZ intersect at V. Use the given information to find the each measure or value. 3. If m WZX = 39.5, find m ZYX. 4. If WX = 8x 5 and WZ = 6x + 3, find x. 23
24 5. JKLM is a rhombus. If m JML = 84 and m JKM = (5x + 16), find the value of x. 24
25 Example 2: Write a paragraph proof. Given: LMNP is a parallelogram. 1 2 and 2 6 Prove: LMNP is a rhombus. Guided Practice 2: Is there enough information given to prove that ABCD is a rhombus? Given: ABCD is a parallelogram. AD DC Prove: ADCD is a rhombus Example 3: GARDENING Hector is measuring the boundary of a new garden. He wants the garden to be square. He has set each of the corner stakes 6 feet apart. What does Hector need to know to make sure that the garden is square? 25
26 Guided Practice 3: Sachin has a shape he knows to be a parallelogram and all four sides are congruent. Which information does he need to know to determine whether it is also a square? A. The diagonal bisects a pair of opposite angles. B. The diagonals bisect each other. C. The diagonals are perpendicular. D. The diagonals are congruent. Classify Quadrilaterals Using Coordinate Geometry Example 4: Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A( 2, 1), B( 1, 3), C(3, 2), and D(2, 2). List all that apply. Explain. Guided Practice 4: Determine whether parallelogram EFGH is a rhombus, a rectangle, or a square for E(0, 2), F( 3, 0), G( 1, 3), and H(2, 1). List all that apply 26
27 More examples: Guided Practice 5. Determine whether parallelogram JKLM with vertices J( 7, 2), K(0, 4), L(9, 2), and M(2, 4) is a rhombus, a rectangle, or a square. List all that apply. Explain (Remember to find distances, slopes, midpoints to help explain.) 27
28 6.6 Trapezoids and Kites Notes Use Properties of Isosceles Trapezoids Example 1: A. BASKET Each side of the basket shown is an isosceles trapezoid. If m JML = 130, KN = 6.7 feet, and MN = 3.6 feet, find m MJK. Example 1: B. BASKET Each side of the basket shown is an isosceles trapezoid. If m JML = 130, KN = 6.7 feet, and MN = 3.6 feet, find JL. 28
29 Guided Practice 1: A. Each side of the basket shown is an isosceles trapezoid. If m FGH = 124, FI = 9.8 feet, and IG = 4.3 feet, find m EFG. Guided Practice 1: B. Each side of the basket shown is an isosceles trapezoid. If m FGH = 124, FI = 9.8 feet, and EG = 14.1 feet, find IH. Example 2: Quadrilateral ABCD has vertices A(5, 1), B( 3, 1), C( 2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. Guided Practice 2: Quadrilateral QRST has vertices Q( 1, 0), R(2, 2), S(5, 0), and T( 1, 4). Determine whether QRST is a trapezoid and if so, determine whether it is an isosceles trapezoid. 29
30 Example 3: In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x? Guided Practice 3: WXYZ is an isosceles trapezoid with median Find XY if JK = 18 and WZ =
31 More examples: The speaker shown is an isosceles trapezoid. If m FJH = 85, FK = 8 inches, and JG = 19 inches, find each measure. 1. m FGH 2. KH Each side of the basket shown is an isosceles trapezoid. If m JML = 130, KN = 6.7 feet, and MN = 3.6 feet, find each measure. 3. m MJK 4. JL 5. In the figure LH is the midsegment of trapezoid FGJK. What is the value of x? 31
32 6. Quadrilateral ABCD has vertices A( 3, 4), B(2, 5), C(3, 3), and D( 1, 0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. 7. Quadrilateral ABCD has vertices A(5, 1), B( 3, 1), C( 2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. 32
33 Example 4: A. If WXYZ is a kite, find m XYZ. Example 4: B. If MNPQ is a kite, find NP. Guided Practice 4: A. If BCDE is a kite, find m CDE. Guided Practice 4: B. If JKLM is a kite, find KL. More examples: 9. If FGHJ is a kite, find m GFJ. 10. If WXYZ is a kite, find ZY. 33
Geometry Chapter 8 8-5: USE PROPERTIES OF TRAPEZOIDS AND KITES
Geometry Chapter 8 8-5: USE PROPERTIES OF TRAPEZOIDS AND KITES Use Properties of Trapezoids and Kites Objective: Students will be able to identify and use properties to solve trapezoids and kites. Agenda
More information6-1. Angles of Polygons. Lesson 6-1. What You ll Learn. Active Vocabulary
6-1 Angles of Polygons What You ll Learn Skim Lesson 6-1. Predict two things that you expect to learn based on the headings and figures in the lesson. 1. 2. Lesson 6-1 Active Vocabulary diagonal New Vocabulary
More informationGeometry - Chapter 6 Review
Class: Date: Geometry - Chapter 6 Review 1. Find the sum of the measures of the angles of the figure. 4. Find the value of x. The diagram is not to scale. A. 1260 B. 900 C. 540 D. 720 2. The sum of the
More information16. DOK 1, I will succeed." In this conditional statement, the underlined portion is
Geometry Semester 1 REVIEW 1. DOK 1 The point that divides a line segment into two congruent segments. 2. DOK 1 lines have the same slope. 3. DOK 1 If you have two parallel lines and a transversal, then
More informationWarm-Up Exercises. Find the value of x. 1. ANSWER 65 ANSWER 120
Warm-Up Exercises Find the value of x. 1. 65 2. 120 Warm-Up Exercises Find the value of x. 3. 70 EXAMPLE Warm-Up 1Exercises Identify quadrilaterals Quadrilateral ABCD has at least one pair of opposite
More informationUnit 6 Quadrilaterals
Unit 6 Quadrilaterals ay lasswork ay Homework Monday Properties of a Parallelogram 1 HW 6.1 11/13 Tuesday 11/14 Proving a Parallelogram 2 HW 6.2 Wednesday 11/15 Thursday 11/16 Friday 11/17 Monday 11/20
More informationGeometry Unit 5 Practice Test
Name: Class: Date: ID: X Geometry Unit 5 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x in the rectangle? Hint: use
More informationSecondary 2 Unit 7 Test Study Guide
Class: Date: Secondary 2 Unit 7 Test Study Guide 2014-2015 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement can you use to conclude that
More informationGeometry Tutor Worksheet 9 Quadrilaterals
Geometry Tutor Worksheet 9 Quadrilaterals 1 Geometry Tutor - Worksheet 9 - Quadrilaterals 1. Which name best describes quadrilateral DEFG? 2. Which name best describes quadrilateral ABCD? 3. Which name
More informationGeometry Topic 4 Quadrilaterals and Coordinate Proof
Geometry Topic 4 Quadrilaterals and Coordinate Proof MAFS.912.G-CO.3.11 In the diagram below, parallelogram has diagonals and that intersect at point. Which expression is NOT always true? A. B. C. D. C
More information6-3 Conditions for Parallelograms
Warm Up Justify each statement. 1. 2. Reflex Prop. of Conv. of Alt. Int. s Thm. Evaluate each expression for x = 12 and y = 8.5. 3. 2x + 7 4. 16x 9 31 183 5. (8y + 5) 73 Objective Prove that a given quadrilateral
More information6. Which angles in the diagram are congruent to 1? Choose all that apply. 2. m YKZ
PRYZ is a rhombus. If RK = 5, RY = 13 and m YRZ = 67, find each measure. Quadrilateral GHJK is a rectangle and m 1 = 37. 1. KY 6. Which angles in the diagram are congruent to 1? Choose all that apply.
More informationDownloaded from
1 IX Mathematics Chapter 8: Quadrilaterals Chapter Notes Top Definitions 1. A quadrilateral is a closed figure obtained by joining four points (with no three points collinear) in an order. 2. A diagonal
More information6-6 Trapezoids and Kites. CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 25. WP
CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 25. WP By the Pythagorean Theorem, WP 2 = WX 2 XP 2 = 6 2 4 2 = 20 27. A kite can only have one pair of opposite congruent angles and Let m X = m
More informationIndicate whether the statement is true or false.
MATH 121 SPRING 2017 - PRACTICE FINAL EXAM Indicate whether the statement is true or false. 1. Given that point P is the midpoint of both and, it follows that. 2. If, then. 3. In a circle (or congruent
More informationUnit 6: Quadrilaterals
Name: Period: Unit 6: Quadrilaterals Geometry Honors Homework Section 6.1: Classifying Quadrilaterals State whether each statement is true or false. Justify your response. 1. All squares are rectangles.
More information(A) Circle (B) Polygon (C) Line segment (D) None of them (A) (B) (C) (D) (A) Understanding Quadrilaterals <1M>
Understanding Quadrilaterals 1.A simple closed curve made up of only line segments is called a (A) Circle (B) Polygon (C) Line segment (D) None of them 2.In the following figure, which of the polygon
More informationDiscussion: With a partner, discuss what you believe a parallelogram is? Parallelogram Definition:
Name: Ms. Ayinde Date: Geometry CC 4.2: Properties of Parallelograms Objective: To recognize and apply properties of sides, angles, and diagonals of parallelograms. To determine the area and perimeter
More information(A) Circle (B) Polygon (C) Line segment (D) None of them
Understanding Quadrilaterals 1.The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60 degree. Find the angles of the parallelogram.
More informationRegents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2
Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 www.jmap.org Name: G.G.69: Quadrilaterals in the Coordinate Plane 2: Investigate the properties of quadrilaterals in the coordinate
More informationGEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)
GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance
More informationJK XY LJ LJ ZX KL KL YZ LJ KL YX KJ. Final Exam Review Modules 10 16, 18 19
Geometry Final Exam Review Modules 10 16, 18 19 Use the following information for 1 3. The figure is symmetric about the x axis. Name: 6. In this figure ~. Which statement is not true? A JK XY LJ ZX C
More informationAnalytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6
DOE Assessment Guide Questions (2015) Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6 Question Example Item #1 Which transformation of ΔMNO results in a congruent triangle? Answer Example
More information9.5 Properties and Conditions for Kites and Trapezoids
Name lass ate 9.5 Properties and onditions for Kites and Trapezoids ssential uestion: What are the properties of kites and trapezoids? Resource Locker xplore xploring Properties of Kites kite is a quadrilateral
More information9.1 Properties of Parallelograms
Name lass ate 9.1 Properties of Parallelograms Essential Question: What can you conclude about the sides, angles, and diagonals of a parallelogram? Explore Investigating Parallelograms quadrilateral is
More information3. Given the similarity transformation shown below; identify the composition:
Midterm Multiple Choice Practice 1. Based on the construction below, which statement must be true? 1 1) m ABD m CBD 2 2) m ABD m CBD 3) m ABD m ABC 1 4) m CBD m ABD 2 2. Line segment AB is shown in the
More information6-5 P R OV I N G R H O M B U S E S, R E C TA N G L E S, A N D S Q UA R E S
6-5 P R OV I N G R H O M B U S E S, R E C TA N G L E S, A N D S Q UA R E S Workbook page 261, number 13 Given: ABCD is a rectangle Prove: EDC ECD A D E B C Statements Reasons 1) ABCD is a rectangle 1)
More information1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable
Four sided polygon 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Foldable The fold crease 2. Now, divide the right hand section
More information11.2 Areas of Trapezoids,
11. Areas of Trapezoids, Rhombuses, and Kites Goal p Find areas of other types of quadrilaterals. Your Notes VOCABULARY Height of a trapezoid THEOREM 11.4: AREA OF A TRAPEZOID b 1 The area of a trapezoid
More informationPolygon Unit Test Review
Name Hour Polygon Unit Test Review Directions: You must show all work for all problems below. For the problems where you have a quadrilateral and use their properties, justify the set up, and provide the
More information6.1 Ratios, Proportions, and the Geometric Mean
6.1 Ratios, Proportions, and the Geometric Mean VOCABULARY Ratio of a to b Proportion Means and Extremes Geometric Mean EX1: Simplify Ratios Simplify the ratio. (See Table of Measures, p. 921) a. 76 cm:
More informationSOLUTION: The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore,
Find each measure. 1. The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore, 2. WT, if ZX = 20 and TY = 15 The trapezoid WXYZ is an isosceles trapezoid. So,
More informationAreas of Tropezoids, Rhombuses, and Kites
102 Areas of Tropezoids, Rhombuses, and Kites MathemaHcs Florida Standards MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MP1. MP3, MP 4,MP6 Objective
More informationGeometry. Warm Ups. Chapter 11
Geometry Warm Ups Chapter 11 Name Period Teacher 1 1.) Find h. Show all work. (Hint: Remember special right triangles.) a.) b.) c.) 2.) Triangle RST is a right triangle. Find the measure of angle R. Show
More informationDate: Period: Quadrilateral Word Problems: Review Sheet
Name: Quadrilateral Word Problems: Review Sheet Date: Period: Geometry Honors Directions: Please answer the following on a separate sheet of paper. Completing this review sheet will help you to do well
More information0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?
0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB # AC. The measure of!b is 40. 1) a! b 2) a! c 3) b! c 4) d! e What is the measure of!a? 1) 40 2) 50 3) 70
More informationTrapezoids and Kites. isosceles trapezoid. You are asked to prove the following theorems in the exercises.
Page 1 of 8 6.5 Trapezoids and ites What you should learn O 1 Use properties of trapezoids. O 2 Use properties of kites. Why you should learn it To solve real-life problems, such as planning the layers
More informationAW Math 10 UNIT 6 SIMILARITY OF FIGURES
AW Math 10 UNIT 6 SIMILARITY OF FIGURES Assignment Title Work to complete Complete 1 Review Proportional Reasoning Cross Multiply and Divide 2 Similar Figures Similar Figures 3 4 Determining Sides in Similar
More information3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm.
1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationReview Questions for Unit Exam 32 Geometry
Review Questions for Unit Exam 32 Geometry 1.Intheaccompanyingdiagramof parallelogramabcd,diagonals AC and BD intersectate,ae&=3x& 4,andEC&=x&+12. Whatisthevalueofx? (1)8 (3)20 (2)16 (4)40 2.Intheaccompanyingdiagramof
More informationWhat You ll Learn. Why It s Important
Many artists use geometric concepts in their work. Think about what you have learned in geometry. How do these examples of First Nations art and architecture show geometry ideas? What You ll Learn Identify
More information1. Write the angles in order from 2. Write the side lengths in order from
Lesson 1 Assignment Triangle Inequalities 1. Write the angles in order from 2. Write the side lengths in order from smallest to largest. shortest to longest. 3. Tell whether a triangle can have the sides
More informationGeometry 2001 part 1
Geometry 2001 part 1 1. Point is the center of a circle with a radius of 20 inches. square is drawn with two vertices on the circle and a side containing. What is the area of the square in square inches?
More informationA. 100 B. 110 C. 115 D. 145 E. 210
Practice Quiz Polygons Area Perimeter Volume 1. Two angles of a hexagon measure 140 each. The other four angles are equal in measure. What is the measure of each of the other four equal angles, in degrees?
More informationHonors Geometry Chapter 6 Supplement. Q (4x) (5x)
Honors Geometry hapter 6 upplement Name: 1. Given: Q m Q = (4x) m Q = (5x) m Q = 40 m Q = 32 Find the value of x, m Q, m Q, m Q Q (4x) (5x) 40 32 2. Given: m = (8x + 20) m = (150 6x) m = (12x + 60) a)
More informationGeometry. a) Rhombus b) Square c) Trapezium d) Rectangle
Geometry A polygon is a many sided closed shape. Four sided polygons are called quadrilaterals. Sum of angles in a quadrilateral equals 360. Parallelogram is a quadrilateral where opposite sides are parallel.
More informationFSA Geometry EOC Getting ready for. Circles, Geometric Measurement, and Geometric Properties with Equations.
Getting ready for. FSA Geometry EOC Circles, Geometric Measurement, and Geometric Properties with Equations 2014-2015 Teacher Packet Shared by Miami-Dade Schools Shared by Miami-Dade Schools MAFS.912.G-C.1.1
More informationUNIT 6 SIMILARITY OF FIGURES
UNIT 6 SIMILARITY OF FIGURES Assignment Title Work to complete Complete Complete the vocabulary words on Vocabulary the attached handout with information from the booklet or text. 1 Review Proportional
More informationAssignment Assigned Date Due Date Grade 4.7 Worksheet
Geometry Unit 4 and 5: Packet 2 QUADRILATERALS This is a packet containing the homework and some classwork for the first half of the first unit of geometry. This MUST be completed and turned in before
More informationThe area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2.
ALGEBRA Find each missing length. 21. A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base? The area A of a trapezoid
More informationThe Quadrilateral Detective
The Quadrilateral Detective a Coordinate Geometry Activity An object might certainly LOOK like a square, but how much information do you really need before you can be absolutely sure that it IS a square?
More information18 Two-Dimensional Shapes
18 Two-Dimensional Shapes CHAPTER Worksheet 1 Identify the shape. Classifying Polygons 1. I have 3 sides and 3 corners. 2. I have 6 sides and 6 corners. Each figure is made from two shapes. Name the shapes.
More information0810ge. Geometry Regents Exam y # (x $ 3) 2 % 4 y # 2x $ 5 1) (0,%4) 2) (%4,0) 3) (%4,%3) and (0,5) 4) (%3,%4) and (5,0)
0810ge 1 In the diagram below, ABC! XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements
More informationGEOMETRY. Workbook Common Core Standards Edition. Published by TOPICAL REVIEW BOOK COMPANY. P. O. Box 328 Onsted, MI
Workbook Common Core Standards Edition Published by TOPICAL REVIEW BOOK COMPANY P. O. Box 328 Onsted, MI 49265-0328 www.topicalrbc.com EXAM PAGE Reference Sheet...i January 2017...1 June 2017...11 August
More informationAre You Ready? Find Perimeter
SKILL 3 Find Perimeter Teaching Skill 3 Objective Find the perimeter of figures. Instruct students to read the definition at the top of the page. Stress that the shape of the figure does not matter the
More information6.2 Slopes of Parallel and Perpendicular Lines
. Slopes of Parallel and Perpendicular Lines FOCUS Use slope to find out if two lines are parallel or perpendicular. These two lines are parallel. Slope of line AB Slope of line CD These two lines have
More informationTitle: Quadrilaterals Aren t Just Squares
Title: Quadrilaterals ren t Just Squares Brief Overview: This is a collection of the first three lessons in a series of seven lessons studying characteristics of quadrilaterals, including trapezoids, parallelograms,
More informationGeometry - Midterm Exam Review - Chapters 1, 2
Geometry - Midterm Exam Review - Chapters 1, 2 1. Name three points in the diagram that are not collinear. 2. Describe what the notation stands for. Illustrate with a sketch. 3. Draw four points, A, B,
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 17, :30 to 3:30 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 17, 2017 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of any communications
More informationSemester 1 Final Exam Review
Target 1: Vocabulary and notation Semester 1 Final Exam Review Name 1. Find the intersection of MN and LO. 2. 3) Vocabulary: Define the following terms and draw a diagram to match: a) Point b) Line c)
More informationFair Game Review. Chapter 7. Name Date
Name Date Chapter 7 Fair Game Review Use a protractor to find the measure of the angle. Then classify the angle as acute, obtuse, right, or straight. 1. 2. 3. 4. 5. 6. 141 Name Date Chapter 7 Fair Game
More informationMEA 501 LESSON _NOTES Period. CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 301 Compute the perimeter of polygons when all
MEA 501 LESSON _NOTES Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 301 Compute the perimeter of polygons when all attain mastery at this level side lengths are given MEA 302 Compute
More information1. What term describes a transformation that does not change a figure s size or shape?
1. What term describes a transformation that does not change a figure s size or shape? () similarity () isometry () collinearity (D) symmetry For questions 2 4, use the diagram showing parallelogram D.
More information8.3 Prove It! A Practice Understanding Task
15 8.3 Prove It! A Practice Understanding Task In this task you need to use all the things you know about quadrilaterals, distance, and slope to prove that the shapes are parallelograms, rectangles, rhombi,
More informationGeometry Midterm Review Spring 2011 Name Date Period. 2. Name three points that are collinear Name a pair of opposite rays. 3.
Name Date Period Unit 1 1. Give two other names for AB. 1. 2. Name three points that are collinear. 2. 3. Name a pair of opposite rays. 3. 4. Give another name for CD. 4. Point J is between H and K on
More informationUnit 7 Scale Drawings and Dilations
Unit 7 Scale Drawings and Dilations Day Classwork Day Homework Friday 12/1 Unit 6 Test Monday 12/4 Tuesday 12/5 Properties of Scale Drawings Scale Drawings Using Constructions Dilations and Scale Drawings
More informationName Period Date. GEOMETRY AND MEASURESUREMENT Student Pages for Packet 6: Drawings and Constructions
Name Period Date GEOMETRY AND MEASURESUREMENT Student Pages for Packet 6: Drawings and Constructions GEO6.1 Geometric Drawings Review geometric notation and vocabulary. Use a compass and a ruler to make
More informationLesson 1 Area of Parallelograms
NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture
More informationGEOMETRY (Common Core)
GEOMETRY (COMMON CORE) Network 603 PRACTICE REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Practice Exam Student Name: School Name: The possession or use of any communications device is strictly
More informationAngles formed by Transversals
Section 3-1: Parallel Lines and Transversals SOL: None Objectives: Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal Vocabulary: Parallel
More informationExtra Practice 1. Name Date. Lesson 8.1: Parallel Lines. 1. Which line segments are parallel? How do you know? a) b) c) d)
Master 8.24 Extra Practice 1 Lesson 8.1: Parallel Lines 1. Which line segments are parallel? How do you know? a) b) c) d) 2. Look at the diagram below. Find as many pairs of parallel line segments as you
More informationProject Maths Geometry Notes
The areas that you need to study are: Project Maths Geometry Notes (i) Geometry Terms: (ii) Theorems: (iii) Constructions: (iv) Enlargements: Axiom, theorem, proof, corollary, converse, implies The exam
More informationTo Explore the Properties of Parallelogram
Exemplar To Explore the Properties of Parallelogram Objective To explore the properties of parallelogram Dimension Measures, Shape and Space Learning Unit Quadrilaterals Key Stage 3 Materials Required
More informationActivity 11 OBJECTIVE. MATERIAL REQUIRED Cardboard, white paper, graph paper with various given points, geometry box, pen/pencil.
Activity 11 OBJECTIVE To find the values of abscissae and ordinates of various points given in a cartesian plane. MATERIAL REQUIRED Cardboard, white paper, graph paper with various given points, geometry
More informationSTRAND H: Angle Geometry
Mathematics SKE, Strand H UNIT H3 onstructions and Loci: Text STRND H: ngle Geometry H3 onstructions and Loci Text ontents Section H3.1 Drawing and Symmetry H3.2 onstructing Triangles and ther Shapes H3.3
More informationAll in the Family. b. Use your paper tracing to compare the side lengths of the parallelogram. What appears to be true? Summarize your findings below.
The quadrilateral family is organized according to the number pairs of sides parallel in a particular quadrilateral. Given a quadrilateral, there are three distinct possibilities: both pairs of opposite
More information3 Kevin s work for deriving the equation of a circle is shown below.
June 2016 1. A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation?
More informationName: Date: Chapter 2 Quiz Geometry. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: Chapter 2 Quiz Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x? Identify the missing justifications.,, and.
More informationKCATM Geometry
Name School KCATM Geometry 9 10 2013 1) Find the minimum perimeter of a rectangle whose area is 169 square meters. a) 42 meters b) 13 meters c) 26 meters d) 52 meters 2) Find the coordinates of the midpoint
More information3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the value of m. 1. 2. 3. 4. undefined 0 Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular
More informationFINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true.
FINL RVIW 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. c) oth
More informationParallels and Euclidean Geometry
Parallels and Euclidean Geometry Lines l and m which are coplanar but do not meet are said to be parallel; we denote this by writing l m. Likewise, segments or rays are parallel if they are subsets of
More information(Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions.
Seventh Grade Mathematics Assessments page 1 (Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions. A. TLW use tools to draw squares, rectangles, triangles and
More informationGeometry 1 FINAL REVIEW 2011
Geometry 1 FINL RVIW 2011 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram.
More informationPRE-JUNIOR CERTIFICATE EXAMINATION, 2010 MATHEMATICS HIGHER LEVEL. PAPER 2 (300 marks) TIME : 2½ HOURS
J.20 PRE-JUNIOR CERTIFICATE EXAMINATION, 2010 MATHEMATICS HIGHER LEVEL PAPER 2 (300 marks) TIME : 2½ HOURS Attempt ALL questions. Each question carries 50 marks. Graph paper may be obtained from the superintendent.
More informationGeometry Benchmark Assessment #1
Geometry Benchmark Assessment #1 Multiple Choice Circle the letter of the choice that best completes the statement or answers the question. 1. When the net is folded into the rectangular prism shown beside
More informationWorksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics
Worksheet 10 Memorandum: Construction of Geometric Figures Grade 9 Mathematics For each of the answers below, we give the steps to complete the task given. We ve used the following resources if you would
More informationPRIMARY MATHS SERIES
PRIMARY MATHS SERIES REVISION GUIDE FOR STANDARDS 7 AND 8 Elijah M. Michieka And Paul Otinga www.kenpro.org Nairobi, Kenya Kenya Projects Organization (KENPRO) is committed to the noble ideals of sharing
More information#2. Rhombus ABCD has an area of 464 square units. If DB = 18 units, find AC. #3. What is the area of the shaded sector if the measure of <ABC is 80?
1 Pre-AP Geometry Chapter 12 Test Review Standards/Goals: F.1.a.: I can find the perimeter and area of common plane figures, such as: triangles, quadrilaterals, regular polygons, and irregular figures,
More informationParallel Lines Chapter Problems
Parallel Lines Chapter Problems Lines: Intersecting, parallel & skew Class Work Use image 1 1. Name all segments parallel to GH : 2. Name all segments skew to GH : 3. Name all segments intersecting with
More informationProblem of the Month: Between the Lines
Problem of the Month: Between the Lines Overview: In the Problem of the Month Between the Lines, students use polygons to solve problems involving area. The mathematical topics that underlie this POM are
More informationGeometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1
Postulates and Theorems from Chapter 1 Postulate 1: The Ruler Postulate 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. 2. Once
More information11.2 Areas of Trapezoids and Kites
Investigating g Geometry ACTIVITY Use before Lesson 11.2 11.2 Areas of Trapezoids and Kites MATERIALS grap paper straigtedge scissors tape Q U E S T I O N How can you use a parallelogram to find oter areas?
More informationJune 2016 Regents GEOMETRY COMMON CORE
1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? 4) 2
More informationDownloaded from
Understanding Elementary Shapes 1 1.In the given figure, lines l and m are.. to each other. (A) perpendicular (B) parallel (C) intersect (D) None of them. 2.a) If a clock hand starts from 12 and stops
More informationGeometry Semester 2 Final Review
Class: Date: Geometry Semester 2 Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Each unit on the map represents 5 miles. What
More informationMadinaty Language School Math Department 4 th primary Revision sheet 4 th primary Complete : 1) 5 million, 34 thousand,and 18 =.. 2) is the smallest
Madinaty Language School Math Department 4 th primary Revision sheet 4 th primary Complete : 1) 5 million, 34 thousand,and 18 =.. 2) is the smallest prime no. 3) is common factor of all nos. 4) The factors
More informationGeometry in Construction. 2. Graph the equations below. a) b) y = 3x + 1 y = -2x + 3
Unit 4 Geometry in Construction Name Block 1. The LHS River Watch club wants to fence in an area along the Thompson riverbank to protect some endangered riverbank. The club has enough money to buy 200
More informationLength and area Block 1 Student Activity Sheet
Block 1 Student Activity Sheet 1. Write the area and perimeter formulas for each shape. 2. What does each of the variables in these formulas represent? 3. How is the area of a square related to the area
More informationGeometer s Skethchpad 7th Grade Guide to Learning Geometry
Geometer s Skethchpad 7th Grade Guide to Learning Geometry This Guide Belongs to: Date: 2 -- Learning with Geometer s Sketchpad **a story can be added or one could choose to use the activities alone and
More information